The surviving spouse, or any other legally designated representative, of an employee who is eligible for participation in an Early Retirement Incentive Program may exercise the employee's option to participate when the employee dies or is determined to be mentally incompetent subsequent to the adoption of the ordinance enacting the Early Retirement Incentive Program but prior to the deadline for electing to participate in the program, provided the spouse or representative executes the participation agreement on behalf of the employee. In such cases, the employee's department head, subject to approval by the City Manager, shall establish the actual date of retirement.